Part of the Units & Conversions suite · 14 calculators
Radians to Turns Converter
Convert radians to full turns — divide by 2π. Results update as you type; exact factors shown.
One radian is 0.1592 turn (revolution) — see the exact factor, not a rounded rule of thumb.
Convert angle
Direction
Results update as you type
Results
1 rad in turn (revolution)
0.1592 rev
Conversion factor—
Reverse conversion—
In radian (base unit)—
Reviewed September 2026. Exact conversion factors from the BIPM SI Brochure and NIST SP 811; Australia is fully metric under the National Measurement Act 1960; imperial units appear only in trade with the US and in older documents.
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About angle conversion
Method
How the radians to turns converter works
Angles convert through the radian. A full turn is 2π radians = 360° = 400 gon = 6,400 NATO mils. A degree is 60 arcminutes, an arcminute 60 arcseconds.
Australia is fully metric under the National Measurement Act 1960; imperial units appear only in trade with the US and in older documents.
Data
Common angle conversions
| From | To | Units |
|---|---|---|
| 0.7854 rad | 0.125 rev | radians to turn (revolution) |
| 1.5708 rad | 0.25 rev | radians to turn (revolution) |
| 3.1416 rad | 0.5 rev | radians to turn (revolution) |
| 4.7124 rad | 0.75 rev | radians to turn (revolution) |
| 6.2832 rad | 1 rev | radians to turn (revolution) |
| 9.4248 rad | 1.5 rev | radians to turn (revolution) |
| 12.566 rad | 1.9999 rev | radians to turn (revolution) |
| 15.708 rad | 2.5 rev | radians to turn (revolution) |
| 31.416 rad | 5 rev | radians to turn (revolution) |
| 62.832 rad | 10 rev | radians to turn (revolution) |
| 100 rad | 15.9155 rev | radians to turn (revolution) |
| 628.32 rad | 100.0002 rev | radians to turn (revolution) |
Data
Units in this converter and their exact factors
| Unit | Symbol | One unit in radians |
|---|---|---|
| degree | ° | 0.0174532925 radian |
| radian | rad | 1 radian |
| gradian (gon) | gon | 0.0157079633 radian |
| arcminute | ′ | 0.0002908882 radian |
| arcsecond | ″ | 0.0000048481 radian |
| turn (revolution) | rev | 6.2831853072 radian |
| NATO mil (1/6400 turn) | mil | 0.0009817477 radian |
FAQFrequently asked questions about angle conversion
How many radians in a turn?
2π, about 6.2832.
What is π radians in turns?
Half a turn.
What is 6.2832 radians?
Exactly one full turn.
Where are turns used?
Rotational mechanics, where revolutions are the natural count, and in gearing.
What is 100 radians?
15.92 turns.
Sources
Where these figures come from
- BIPM — The International System of Units (SI Brochure, 9th edition) — definitions of the base and derived units.
- NIST Special Publication 811 — Guide for the Use of the International System of Units — the exact conversion factors used here.
- National Measurement Institute (NMI) — Australia's national measurement authority.
Last checked: September 2026. Conversion factors are fixed by definition and do not change with tax years or regulations.